DotProduct - Maple Help

Student[MultivariateCalculus]

 DotProduct
 return the dot product of two vectors

 Calling Sequence DotProduct(u, v, conjopt) u . v

Parameters

 u, v - Vectors with algebraic entries and equal dimensions conjopt - (optional) a keyword argument of the form conjugate = truefalse; defaults to false

Description

 • The DotProduct command computes the dot product of u and v.
 • The infix operator . can also be used to compute the dot product.
 • If u and v are $n$-dimensional Vectors, and conjugate is false, their dot product is given by the formula $\sum _{i=1}^{n}{u}_{i}{v}_{i}$. If conjugate is true, then their dot product is given by the formula $\sum _{i=1}^{n}\stackrel{&conjugate0;}{{u}_{i}}{v}_{i}$.

Examples

 > $\mathrm{with}\left(\mathrm{Student}:-\mathrm{MultivariateCalculus}\right):$
 > $u≔⟨a,b,c⟩$
 ${u}{≔}\left[\begin{array}{c}{a}\\ {b}\\ {c}\end{array}\right]$ (1)
 > $v≔⟨d,e,f⟩$
 ${v}{≔}\left[\begin{array}{c}{d}\\ {e}\\ {f}\end{array}\right]$ (2)
 > $u·v$
 ${a}{}{d}{+}{b}{}{e}{+}{c}{}{f}$ (3)

The complex dot product is not commutative.

 > $\mathrm{DotProduct}\left(u,v,\mathrm{conjugate}=\mathrm{true}\right)$
 $\stackrel{{&conjugate0;}}{{a}}{}{d}{+}\stackrel{{&conjugate0;}}{{b}}{}{e}{+}\stackrel{{&conjugate0;}}{{c}}{}{f}$ (4)
 > $\mathrm{DotProduct}\left(v,u,\mathrm{conjugate}=\mathrm{true}\right)$
 $\stackrel{{&conjugate0;}}{{d}}{}{a}{+}\stackrel{{&conjugate0;}}{{e}}{}{b}{+}\stackrel{{&conjugate0;}}{{f}}{}{c}$ (5)

Compatibility

 • The Student[MultivariateCalculus][DotProduct] command was introduced in Maple 2016.